Yayati was a notable ancestor of the warring cousins. In the Mahabharata his story is told in the Sambhava Parva of the Adi Parva starting from Section LXXVIII. The following is a summary from the translation by Kisari Mohan Ganguli, available online.  The story of Yayati appears in various retellings of the Mahabharata as well as in independent works of literature.
Devayani was the daughter of Sukracharya, the preceptor to the Asuras. Sarmishtha was the daughter of Vrishaparvan, the king of the Asuras. Following a childish squabble Sarmishtha threw Devayani in a well. King Yayati, who had been hunting in the area, helped Devayani out. Burning with revenge, Devayani emotionally blackmailed her father into threatening to withdraw his support to the Asuras if her wishes were not met.
Vrishaparvan readily consented to give Devayani whatever she wanted and the brahmin’s daughter demanded, “I desire Sarmishtha with a thousand maids to wait on me!” In order to prevent a calamity falling on her clan, Sarmishtha readily fulfilled Devayani’s wish.
Then Devayani accosted Yayati in the woods and proposed marriage. Yayati pointed out that she was not only a brahmin but the daughter of a very learned brahmin. Therefore he would not be a suitable match for her. He also had misgivings because brahmins were known for pronouncing curses at will. Devayani clarified that Yayati was the son of a brahmin and therefore a brahmin. Though not explicitly stated at this point in the narrative, this refers to Yayati being born due to the blessings of sage Angiras. This is today interpreted in a literal sense, but more likely refers to the practice of niyoga or surrogate fatherhood. Ultimately the two get married. There is no mention of romance or sexual attraction in the narrative. The whole affair is as cold and calculated as the negotiation of business deal.
In due course Devayani bears a son. Perturbed that she will be left childless, Sarmishtha convinces Yayati that he is duty bound to beget a child from her. Again, there is no seduction or attraction, only reasoning. Sarmishtha also bears a son. She tells Devayani that the father of the child was a resplendent ascetic. Thus Yayati sired Yadu and Turvasu from Devayani and Drahyu, Anu and Puru from Sarmishtha.
Once Devayani chanced to meet the children of Sarmishtha and from them learned of their parentage. Devayani went to her father, who pronounced a curse on Yayati making him lose his youth. The King immediately became decrepit. Yayati pleaded that he had not yet been satisfied by youth or Devayani, so Sukracharya added this escape route: “But if thou likest, thou art competent to transfer this thy decrepitude to another.”
Yayati summoned his sons and said that he had not yet been gratified with the enjoyment of youth. He asked one of them to give up his youth for the King’s old age. Yadu, Turvasu, Drahyu and Anu refused and were handed out various curses. Puru exchanged his youth for his father’s old age without demur and was appointed heir and blessed with long life, fame and numerous progeny.
For ‘a thousand years’ Yayati ruled well but also indulged in the pleasures of life. Then he returned youth to Puru, gave him the throne and ascended to heaven. The tale of Yayati continues there, but that is another story. The Pandavas and the Kauravas were from descendants of Puru.